Abstract
Evaluating the time-delay, Doppler effect and carrier phase of a received signal is a challenging estimation problem that was addressed in a large variety of remote sensing applications. This problem becomes more difficult and less understood when the signal is reflected off one or multiple surfaces and interferes with itself at the receiver stage. This phenomenon might deteriorate the overall system performance, as for the multipath effect in Global Navigation Satellite Systems (GNSS), and mitigation strategies must be accounted for. In other applications such as GNSS reflectometry (GNSS-R) it may be interesting to estimate the parameters of the reflected signal to deduce the geometry and the surface characteristics. In either case, a better understanding of this estimation problem is directly brought by the corresponding lower performance bounds. In the high signal-to-noise ratio regime of the Gaussian conditional signal model, the Cramér-Rao bound (CRB) provides an accurate lower bound in the mean square error sense. In this article, we derive a new compact CRB expression for the joint time-delay and Doppler estimation in a dual source context, considering a band-limited signal and its specular reflection. These compact CRBs are expressed in terms of the baseband signal samples, making them especially easy to use whatever the baseband signal considered, therefore being valid for a variety of remote sensors. This extends existing results in the single source context and opens the door to a plethora of usages to be discussed in the article. The proposed CRB expressions are validated in two representative navigation and radar examples.
Highlights
The joint delay-Doppler estimation problem has been addressed for years as it is a key step in a plethora of applications such as radar, sonar, communications, navigation or remote sensing [1,2,3,4,5,6,7]
It is worth pointing out the impact that having two sources have on the time-delay estimation w.r.t. the single source case, where the threshold region for a Global Positioning System (GPS) signal is at SNR_OUT = 15 dB
A handy closed-form expression of these Cramér-Rao bound (CRB) that only depends on the baseband signal samples was proposed
Summary
The joint delay-Doppler estimation problem has been addressed for years as it is a key step in a plethora of applications such as radar, sonar, communications, navigation or remote sensing [1,2,3,4,5,6,7] This estimation is performed by a receiver in order to localize and track the position of sources such as a transmitting satellite, like in Global Navigation Satellite System (GNSS), or a radiated target from which the system receives the backscattered signal. In challenging realistic scenarios like urban canyons, extended targets or in conventional reflectometry configurations, a series of non-line-of-sight (NLOS) echoes may be collected by the receiver Those echoes, often referred to as multipath, are usually the consequence of good enough reflecting surfaces that are radiated by the sources of interest, which in turn reach the receiver on top of the LOS signals. Both GNSS multipath (i.e., considering one LOS signal and a main secondary path contribution) and the single antenna GNSS-R approach are typical scenarios of a dual source estimation problem, being the main problem of interest in this contribution
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